Precalculus. Mid Unit 3 Review

Front

What is the process for simplifying a rational expression?

Back

To simplify a rational expression, factor the numerator and denominator, cancel any common factors, and express the result in its simplest form.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros of a polynomial function, set the function equal to zero and solve for the variable. This may involve factoring, using the quadratic formula, or other methods.

Front

What does it mean for a zero to have multiplicity?

Back

Multiplicity refers to the number of times a particular zero appears as a root of the polynomial. A zero with multiplicity greater than 1 indicates that the graph touches the x-axis at that point.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial function. If it is positive, the graph rises to the right; if negative, it falls to the right.

Front

What is the difference between a rational expression and a polynomial?

Back

A rational expression is a fraction where the numerator and denominator are polynomials. A polynomial is an expression that consists of variables raised to non-negative integer powers.

Front

How do you perform polynomial long division?

Back

To perform polynomial long division, divide the leading term of the numerator by the leading term of the denominator, multiply the entire denominator by this result, subtract from the numerator, and repeat with the new polynomial.

Front

What is the role of the discriminant in solving quadratic equations?

Back

The discriminant (b² - 4ac) determines the nature of the roots of a quadratic equation. If it is positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

Front

What is the process for factoring a quadratic expression?

Back

To factor a quadratic expression, look for two numbers that multiply to the constant term and add to the linear coefficient. Rewrite the expression as a product of two binomials.

Front

What is the relationship between the degree of a polynomial and the number of zeros?

Back

The degree of a polynomial indicates the maximum number of zeros it can have. A polynomial of degree n can have up to n real zeros.

Front

How do you identify vertical asymptotes in a rational function?

Back

Vertical asymptotes occur at values of x that make the denominator zero (provided the numerator is not also zero at those points).